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If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

User Reshetech
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1 Answer

5 votes

Answer:


5√(3) inches long is the other leg

Explanation:

Given the statement: If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long.

Hypotenuse side = 10 inches

Let length of other leg be x.

Pythagoras theorem states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Then; by definition of Pythagoras theorem;


{\text}(Hypotenuse)^2 = (5)^2 + x^2


(10)^2 = 5^2 + x^2


100 = 25 + x^2

Subtract 25 on both sides we get;


100-25= 25 + x^2-25

Simplify:


75 = x^2

Simplify:


x = √(75) = 5√(3) inches

Therefore, the sides of other leg is
5√(3) inches




User Tpsilva
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